“Unless we win, it doesn’t mean a damn thing,” the would-be Republican presidential nominee warns a campaign rally in South Carolina, despite finishing his fourth month in a row at the top of the polls .

“I want to pick my date for the election. I want it next Tuesday,” he confides to an 11,000-strong crowd typical of the grassroots support that needs to flourish well into March for him to win the Republican nomination, let alone November’s general election.

Such moments of self-doubt are fleeting, however, quickly replaced by the now familiar bombast of a billionaire whose status as a “winner” has become his defining policy platform.

“Nobody has crowds like we have crowds,” he continues, back on message. “It’s a movement. It’s beyond anything.”

Trump is not the only one beginning to wonder whether this improbable campaign can confound the pundits and go the distance, particularly after a burst of recent controversy only seemed to cement his polling lead over his bewildered rivals.

Conventional wisdom holds that any one of Trump’s many outbursts would have sunk most politicians without a trace by now.

If POWs, Fox News and women were not enemies enough, Trump has also accused Mexican immigrants to the US of being rapists ; claimed that a Black Lives Matter protester who was violently ejected from a rally deserved to be “roughed up” ; appeared to mock a New York Times journalist for his disability and then accused the journalist of “ grandstanding ” on that disability in his response; falsely accused Muslim Americans of cheering on the 9/11 attackers; and agreed with suggestions that all such Muslims should have their names tracked on a database .

Trump has complained that many of these incidents were exaggerated by the political media, 70% of whom he says are “scum”. But he has nonetheless refused to retract any of the comments.

“I could have said ‘Oh, I misspoke’, but I am not big on that,” he told the crowd in South Carolina. “You have to be wrong.”

Some rivals still hope that eventually even Trump’s supporters will tire of what critics view as his relentless attacks on minorities in particular. Ohio governor John Kasich, for example, is running attack ads drawing inspiration from anti-Nazi Lutheran pastor Martin Niemöller, whose updated refrain might begin: “First they came for the Mexicans …”

Others question whether there is much over-arching political ideology to Trump at all, as opposed to simple opportunism and a relish for making waves.

“He is an egomaniac, he’s a narcissist, he’s not a conservative, he’s not a liberal, he believes in himself,” former presidential rival Bobby Jindal told the Guardian shortly before dropping out of the race . “He’s not reflective of a coherent ideology, he’s for himself. He took Reagan’s slogan about making America great again, [but] he’s about making Donald Trump.”

Former Florida governor Jeb Bush has accused his nemesis of living in an “alternate universe” designed to “prey on people’s fears”.

Trump, though, seems to prefer the famous political dictum: “Never apologise. Never explain. Just get the thing done and let them howl.” He revels in his poll lead over Kasich and Bush in their home states as if that is all the answer that is needed.

After several weeks of this, other mainstream politicians are beginning to wonder whether howling is going to be enough to stop the Trump juggernaut; whether what started as an extension of Trump’s reality TV fame and scratching an anti-establishment itch has morphed into something far more persistent.

Liz Mair, a Republican strategist who is organising an anti-Trump fundraising committee, worries that many of the comments seen as a gaffes by the liberal media are in fact carefully designed to boost his standing with his core constituency.

“I personally think it’s best that people who don’t like Trump and his policies – whether it’s libertarians like me, establishment Republicans or real, rock-ribbed conservatives – effectively take out an insurance policy and do some work to try to actively undercut him,” she said. “And not just pray for him to commit real political suicide.”

If your campaign is based on jumping the shark, there’s no jumping the shark moment

Unnamed New Hampshire Republican strategist

Another well-connected New Hampshire Republican marvels at the political controversies that Trump has weathered.

“Just one of these flips flops, gaffes or lies, would have killed a capable, competent campaign,” he said. But, he added, “if your campaign is based on jumping the shark, there’s no jumping the shark moment”.

Yet there is more to Trump than attention-grabbing outrage. As he delights in telling his supporters, the three issues he rails against most – immigration reform, free trade deals and Barack Obama’s national security policy – have become perhaps the defining issues of the election.

“Who’s going to be best? Trump,Trump, Trump,” he bragged, to an answering chant from supporters that did nothing to dispel the fascistic overtones of Tuesday’s rally in Myrtle Beach, South Carolina.

His policies for deporting every undocumented immigrant in the US and demanding Mexico pay for a border wall – “A real wall. A very tall wall, taller than that ceiling” – might sound unrealistic, but they have arguably destroyed the campaign hopes of Bush, who favours immigration reform.

So what might it take to stop Trump?

The biggest source of optimism among opponents is the increasing belief that the polling on which Trump draws his confidence is profoundly flawed.

Polls that just ask whether people think Trump is likely to win, rather than whether they would actually vote for him, again show the gap between expectations and reality. Many surveys do not adjust for low turnout levels in primary elections either.

Among Americans who identify as Republicans, polls suggest Trump has 25% to 30% of the vote. A survey from Pew Research conducted at the end of September provided more detail about who those individuals are: they are likely to be less educated and less affluent compared to the support base of other candidates.

Yet Trump’s support base could be problematic on election day. In 2008, Americans who didn’t graduate from college were significantly less likely to register to vote compared to those who did graduate.

It does look like Trump supporters tend to be less educated. But the more detailed the demographic data, the less reliable it is, given that pollsters are struggling to find representative samples of Americans to talk to them.

Those demographics might also explain why college-educated pundits underestimated Trump’s support. There is another cognitive bias, one called “ the curse of knowledge ”, whereby better informed people find it difficult to view problems from the perspective of others who don’t have the same information.

Converting such passionate supporters will be hard. To immediately blunt Trump’s lead, another candidate would need to tap into his support base without jeopardising their own. Polling experts believe this to be unlikely, as it is hard to imagine anyone doing Trump better than Trump, let alone anyone doing Trump without sacrificing their own support.

A far more likely outcome is that Trump’s base remains solid but his relative lead slowly declines as voters coalesce around candidates such Marco Rubio or Ted Cruz. Insiders will become clearer frontrunners and the outsiders will fall behind once the excitement of Iowa or New Hampshire fades, perhaps leaving the real-estate mogul from New York looking as forgotten as winners in these early states in past elections, from Pat Robertson in 1988 to Mike Huckabee in 2008.

This threat can be best understood by looking at responses to the question: “Are there any of these candidates you would definitely not support for the Republican nomination for president?”

While 20%-30% of voters say they would support Trump, another 20%-30% say they definitely would not. Other candidates, like Cruz, aren’t quite so divisive (only 5%-10% say they definitely wouldn’t vote for him).

That means undecided voters are more likely to drift towards candidates other than Trump – a trend likely to be helped by sceptical party leaders who make up 7% of the deciding votes at the GOP national convention.

Prominent Iowa conservative Steve Deace is one of many who think Trump’s ultimate appeal will prove limited.

“Trump’s got a locked-in base no matter what he does,” he said. Deace, a vocal supporter of Cruz, compared Trump to former Texas congressman Ron Paul in that both candidates had “a high floor and a low ceiling”.

Trump’s antics are “both a good and a bad thing”, he argued. “On one hand, it produces a loyal following that is attracted to that persona which will not leave you. On the other hand, it limits your ability to grow beyond that.”

This was echoed by a strategist familiar with Trump’s campaign who believes the trend will eventually lead to a “death by a thousand cuts”.

“He has stable base of support but he can’t expand it and his state polls are not that good,” the strategist said. “I think frankly this harms him from being able to expand his support.”

And even if Trump’s comments don’t impact his campaign’s fortunes, they could hurt the Republican Party as a whole. Ashley Bell, a prominent black Republican who chairs the 20/20 Leaders of America, a group which promotes criminal justice reform on a bipartisan basis, said Trump had already gone “too far to be considered someone that the party can get behind and lead this party with a bigger tent than today”.

For now though, Trump seems to be defying the laws of political gravity and consistently maintaining a lead over a deeply fragmented Republican field.

A win in the Republican primary is far from out of the question. Betting markets put this at 7/1 currently . With a year to go, anyone who calls a Trump general election victory “impossible” should be treated with caution.

Top Republican pollster Frank Luntz suggests that, at this point, the only thing which could hurt Trump is if he is “shown to have hurt people who have worked for him … but his comments, as radical as they may be, won’t have much of an impact since the people supporting him agree with him”.

He speaks the truth, he speaks what people need to hear. He may be a little bold but you can’t sugar-coat things anymore

Sandra Murray of Dubuque, Iowa

Luntz believes Trump speaks for voters who for the first time feel like they have a mouthpiece and like the fact that they feel they are being heard. As the well-respected pollster noted: “Trump says what they’re thinking and the more outrageous he is, the more they agree with him. He’s saying what no politician would say and that’s another reason that they like him.”

That is certainly the feeling among ordinary supporters who have attended his increasingly packed campaign events in recent months.

“I like the way he speaks,” said Sandra Murray of Dubuque, Iowa. “He speaks the truth, he speaks what people need to hear. He may be a little bold but you can’t sugar-coat things anymore. This country is a huge mess and we need to get out of this and honestly he could be the man to do it.”

Other supporters have a simpler attraction.

“Oh, I wish I had big nuts like him,” said Dino Rossi of Newton, Massachusetts. “He’s not afraid of anybody or anything, that’s pretty cool.”